Hmm. It works a little bit now. I added the two Swedish files to /wp-content/languages/motopress-hotel-booking/

motopress-hotel-booking-sv_SE.mo
motopress-hotel-booking-sv_SE.po

But even after translating the accommodation pages – the search and booking system does not seem to work. Do I need to use some special options in WPML to make it work? Duplicate instead of translate pages?

Thank you for figuring out the issues on your own.
Some translations may be missing if the strings were added after the translation was made.
We would be grateful if you add the missing translations by registering here. The translations will be reviewed and included into one of the future plugin updates.
Also here is an article on how to translate the booking plugin with WPML.